Meet Continuous Lattices Revisited

Artur Kornilowicz

University of Bialystok

Summary.

This work is a continuation of formalization of [13]. Theorems from Chapter III, Section 2, pp. 153-156 are proved.

This work has been supported by KBN Grant 8 T11C 018 12.

MML Identifier: WAYBEL30

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.

[2] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.

[3] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.

[4] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.

[5] Grzegorz Bancerek. Bases and refinements of topologies. Journal of Formalized Mathematics, 10, 1998.

[6] Grzegorz Bancerek. The Lawson topology. Journal of Formalized Mathematics, 10, 1998.

[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[10] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.

[11] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.

[12] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.

[13] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. \em A Compendium of Continuous Lattices. Springer-Verlag, Berlin, Heidelberg, New York, 1980.

[14] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.

[15] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.

[16] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.

[17] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.

[18] Artur Kornilowicz. On the topological properties of meet-continuous lattices. Journal of Formalized Mathematics, 8, 1996.

[19] Artur Kornilowicz. Introduction to meet-continuous topological lattices. Journal of Formalized Mathematics, 10, 1998.

[20] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.

[21] Beata Padlewska. Locally connected spaces. Journal of Formalized Mathematics, 2, 1990.

[22] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[23] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[24] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.

[25] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.

[26] Andrzej Trybulec. Baire spaces, Sober spaces. Journal of Formalized Mathematics, 9, 1997.

[27] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.

[28] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.

[29] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[30] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[31] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

[32] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.